Multiculturalism is one of the most flexible words in the political lexicon, meaning whatever the speaker wants it to mean.

To its defenders, it is the principle that people of different faiths and traditions should be able to live side by side, without surrendering their identities. To its detractors, it is the notion that the state should sponsor cultural division, exempting minority groups from certain obligations of citizenship. Viewed this way, multiculturalism is seen as excusing behaviour that should never be tolerated in a civilised democracy.

That is the interpretation given in a speech in Munich yesterday by David Cameron. He drew a direct connection between "the doctrine of state multiculturalism" and the insularity of Muslim communities that can foster terrorism.

Britain, the prime minister said, has "encouraged different cultures to live separate lives" with the effect of "weakening our collective identity". This has contributed to a disorientation among young Muslims that makes them susceptible to extremist preachers. The antidote, according to Mr Cameron, is a more consistent, robust promotion of liberal-democratic values – human rights, religious tolerance, gender equality – and a greater emphasis on shared British cultural attributes. He calls it "active, muscular liberalism".

It is a forcefully worded intervention on a sensitive topic and therefore guaranteed to cause controversy. Probably, that was part of the intention. Uncontroversial pronouncements don't make headlines. But the provocative tone also guarantees a more frenzied debate, which suits the least tolerant forces in society.

It was sad and predictable that Mr Cameron's words were quickly hailed by the far right, anti-Muslim English Defence League, which held a rally in Luton yesterday. Any speech that heartens the fascist fringe must be deemed a failure.

But at one level, Mr Cameron is right. The state should never turn a blind eye to cruelty and crime out of some misguided sense of cultural sensitivity. That is as true in cases of female genital mutilation, forced marriage and "honour killing" as it is in the case of jihadi preaching.

Police, social workers and teachers have all sometimes been guilty of excusing appalling or dangerous behaviour instead of confronting it. Meanwhile, the government has often failed to make the right partnerships with the Muslim community. That is generally because there is no such thing as "the Muslim community", but, rather, a patchwork of communities, with their distinct traditions and beliefs. That is one reason why the Home Office and local government have struggled effectively to manage funds that are meant to promote social cohesion. Misallocated grants can end up in the hands of groups that foster division.

In fairness to Mr Cameron, these problems can reasonably be seen as unintended consequences of multiculturalism. But it is some extrapolation to then say the whole concept has failed.

At the end of his speech, Mr Cameron made an ambitious leap from bemoaning social segregation to blaming government intervention per se. Integration, he maintains, will happen when people from different communities find "common purpose", released from the burden of the state. He stopped short of weaving "muscular liberalism" into the "Big Society", perhaps because he was addressing a foreign audience unfamiliar with his pet project for civic renewal.

But the prime minister cannot seriously believe that big government is the main cause of social division, still less that his cuts agenda solves the problem. He says, for example, that he wants to make sure more immigrants learn English. Who will teach them? The courses are all run by further education colleges whose budgets are being annihilated. At the heart of Mr Cameron's analysis is a sound impulse. He wants the boundaries of acceptable behaviour – cultural, social, political – to be set in line with modern liberal notions of equal rights and then applied, without fear, favour or prejudice to every section of society. Who could disagree?

But wishing it were so will not get him any closer to achieveing that goal. Nor will caricaturing multiculturalism as some sinister big state project to undermine national unity get him closer to fostering collective solidarity.

The problems Mr Cameron identifies are not new. Headline-grabbing rhetorical flourishes are no substitute for policy solutions.